What is the derivative of (sin(x+cos(x))^2) ?

The derivative of (sin(x+cos(x))^2) is 2cos(2x)

What is the first derivative of (sin(x+cos(x))^2) ?

The first derivative of (sin(x+cos(x))^2) is 2cos(2x)

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\frac{d}{d x} ((sin (x) + cos (x))^{2})

2 cos (2 x)

Solution steps

\frac{d}{d x} ((sin (x) + cos (x))^{2})

Simplify

(sin (x) + cos (x))^{2} : 1 + sin (2 x)

= \frac{d}{d x} (1 + sin (2 x))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (1) + \frac{d}{d x} (sin (2 x))

\frac{d}{d x} (1) = 0

\frac{d}{d x} (sin (2 x)) = cos (2 x) \cdot 2

= 0 + cos (2 x) \cdot 2

Simplify

= 2 cos (2 x)

\frac{7 y ^{2} - t ^{2}}{y ^{5}} \frac{d y}{d t} + \frac{t}{2 y ^{4}} = 0

x \to 1 lim (\frac{4}{x + 3})

y^{^{'}} = 8 y^{2} sin (x)

t^{2} (t + 1)^{- 1}

3 x^{\frac{1}{3}}

What is the derivative of (sin(x+cos(x))^2) ?
The derivative of (sin(x+cos(x))^2) is 2cos(2x)
What is the first derivative of (sin(x+cos(x))^2) ?
The first derivative of (sin(x+cos(x))^2) is 2cos(2x)